Analysis of mixed finite element method (MFEM) for solving the generalized fractional reaction–diffusion equation on nonrectangular domains

2019 ◽  
Vol 78 (5) ◽  
pp. 1531-1547 ◽  
Author(s):  
Mostafa Abbaszadeh ◽  
Mehdi Dehghan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Mixed Finite Element ◽  
Reaction Diffusion ◽  
Mixed Finite Element Method ◽  
Reaction Diffusion Equation ◽  
Fractional Reaction ◽  
Element Method

A fast finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction–diffusion equation

2020 ◽  
Vol 11 (02) ◽  
pp. 2050016
Author(s):  
Yaping Zhang ◽  
Jiliang Cao ◽  
Weiping Bu ◽  
Aiguo Xiao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Time Space ◽  
Distributed Order ◽  
Fractional Reaction ◽  
Element Method

In this work, we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction–diffusion equation (2D-DOTSFRDE) with low regularity solution at the initial time. A fast evaluation of the distributed-order time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the sum-of-exponentials. The stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are discussed. For the spatial approximation, the finite element method is employed. The convergence of the corresponding fully discrete scheme is investigated. Finally, some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.

Sign in / Sign up

Export Citation Format

Share Document